Practice Test 5

NYC SHSAT Practice Test, Form A (2018) — Math section (questions 58–114). Problems are re-created in the same styles and difficulty, not copied verbatim. · Added Jun 6, 2026

Practice Test 5

The SHSAT runs about 90 seconds per question. This 24-question set ≈ 36 min — the timer counts up so you can track your pace.

Ratios & Proportional Relationships

A bakery makes muffins and scones in a ratio of 5 : 3. If it makes 200 muffins, how many scones does it make?

100

110

120

130

On a scale drawing of a triangular sail, the two equal sides each measure 10 cm and the third side measures 6 cm. On the actual sail, the two equal sides each measure 35 feet. What is the length of the third side of the actual sail?

18 feet

21 feet

24 feet

28 feet

The sum of three numbers a, b, and c is 63. The ratio of a to b is 2 : 3, and the ratio of b to c is 3 : 4. What is the value of c?

Percents

In a town, 52% of the residents are adults and 65% own a bicycle. Exactly 38% of the residents are adults who own a bicycle. What percent of the residents are children (non-adults) who do NOT own a bicycle?

13%

21%

27%

35%

A metal bolt must have a diameter of 0.05 inch, with an allowable error of 2%. What is the greatest allowable diameter of the bolt?

0.051 inch

0.052 inch

0.055 inch

0.07 inch

The table shows the percent distribution of how long 500 students spend on homework each night. How many of the 500 students spend at least 60 minutes on homework?

Homework time	Percent
Under 30 min	30%
30–59 min	35%
60–89 min	25%
90 min or more	10%

125

150

175

200

The Number System

An unmarked rod is laid end over end to measure a distance of exactly 84 feet. The same rod is used the same way to measure a distance of exactly 56 feet. What is the length of the longest possible rod that can measure both distances exactly?

4 feet

7 feet

14 feet

28 feet

How many positive even factors of 60 are greater than 4 and less than 30?

The fraction 4/7 written as a decimal is 0.571428571428…, repeating in a 6-digit block (571428). What is the 250th digit after the decimal point?

10.

In the set of consecutive integers from 20 to 40, inclusive, how many integers are multiples of neither 2 nor 5?

Expressions & Equations

11.

What is the value of the expression (−2)³ + 2 × (7 − 3)² − 18 ÷ 6 ?

12.

If 5x − 2y = 20, what is y in terms of x?

y = (5/2)x + 10

y = (5/2)x − 10

y = −(5/2)x + 10

y = −(5/2)x − 10

13.

The number line above shows a solution set. Which inequality does the graph represent?

−1 < x < 3

−1 ≤ x < 3

−1 ≤ x ≤ 3

−1 < x ≤ 3

Word Problems & Rates

14.

A cyclist is traveling at 12 meters per second, and 1 kilometer = 1,000 meters. Which of the following calculations gives the cyclist’s speed in kilometers per hour?

(12 × 3,600) ÷ 1,000

(12 × 1,000) ÷ 3,600

12 × 1,000 × 3,600

12 ÷ (1,000 × 3,600)

15.

Working at constant rates, Ben can wash 3 cars in 30 minutes and Tina can wash 4 cars in 20 minutes. Working together, how many cars can they wash in one hour?

16.

Each week, Priya has fixed expenses of $1,500 at her lamp shop. It costs her $80 to make a lamp, and she sells each lamp for $200. What is Priya’s profit if she makes and sells 30 lamps in one week?

$2,100

$3,600

$6,000

$4,500

Geometry

17.

In parallelogram PQRS shown above, the measure of angle Q is 65°. What is the value of x, the measure of angle R?

105

115

125

18.

What is the area, in square units, of the shaded triangle shown on the coordinate grid above?

19.

The figure above shows a right pyramid with a square base measuring 10 centimeters on each side. The slant height of each triangular face is 8 centimeters. What is the total area of the four triangular faces (the surface area excluding the base)?

80 sq cm

160 sq cm

200 sq cm

320 sq cm

20.

On the number line above, the points P, Q, R, and S lie in that order. PQ = 2¾, PS = 8½, and RS = 1¼. What is the distance QR? (The figure is not drawn to scale.)

4¼

4½

4¾

5¼

Statistics & Probability

21.

The table shows the scores of 10 students on a quiz. What is the mean (average) score of the 10 students?

Score	Number of students
95	2
85	3
75	4
65	1

22.

A box contains 3 red marbles, 4 blue marbles, and 5 yellow marbles. Two marbles are drawn at random, one at a time without replacement. What is the probability that neither marble is red?

6/11

3/4

1/2

9/22

23.

The same test was given to three sections of a class. The table shows the lowest score and the range of scores in each section. What is the overall range of all the scores in all three sections?

Section	Lowest score	Range
I	55	28
II	52	33
III	60	19

24.

The bar graph above shows the number of students who own each type of pet. How many more students own the two most common pets combined than own the two least common pets combined?